Pierro della Francesca 1412 1492 Desargues 1591 1661

이탈리아 수학자 • Pierro della Francesca (1412 -1492) • 원근법 (Desargues 1591 -1661)

3, 4차방정식의 해 • Cardano – (Fior), Tartalia(Fontana)와 경쟁 3, 4차 방정식의 해 solution of x 3 + mx = n. • Notice that (a - b)3 + 3 ab(a - b) = a 3 - b 3 so if a and b satisfy 3 ab = m and a 3 - b 3 = n then a - b is a solution of x 3 + mx = n. But now b = m/3 a so a 3 - m 3/27 a 3 = n, i. e. a 6 - na 3 - m 3/27 = 0. Then x = a - b is the solution to the cubic. • 복소수 문제

Königsberg bridges

Fourier series

새로운 기하학 • • 유클리드의 5개의 가정 칸트 (critiques of pure reason) Saccheri (1667 -1733) 가우스, Lambert, Lobachevsky, 볼리아이 • 리만 • Beltrami, Klein

Euclidean Axioms 1. To draw a straight line from any point to any 2. 3. 4. 5. other. To produce a finite straight line continuously in a straight line. To describe a circle with any centre and distance. That all right angles are equal to each other. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

새로운 수 (대수학) • • • 오일러: 허수, 무리수 코시: 복소 해석학 가우스 Boole Hamilton (quaternion), Clifford (octanion, biquaternion, Clifford algebra) • Cayley, Sylvester (벡터, matrix algebra) • Group, ring, module, field, algebra, Lie group

복소수, quaternion

수의 정의 • Cantor (ordinal, cardinal) • Dedekind (Real number system) • Russel, Whitehead 집합론 {} {{}, {{}}}, {{}}, {{{}}}}, ….